Tail Dependence Functions of Two Classes of Bivariate Skew Distributions

Xin Lao, Zuoxiang Peng and Saralees Nadarajah ()
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Xin Lao: University of Shanghai for Science and Technology
Zuoxiang Peng: Southwest University
Saralees Nadarajah: University of Manchester

Methodology and Computing in Applied Probability, 2023, vol. 25, issue 1, 1-24

Abstract: Abstract The tail dependence function, one method of measuring the strength of extremal dependence between two or more random variables, is attracting an increasing attention in risk management. In this paper, we focus on the asymptotics of tail dependence functions of bivariate skew quasi elliptical and bivariate half-skew elliptical random vectors. The tail dependence functions of the two classes of bivariate skew random vectors are derived. Further, the decay rates of the tail dependence functions are derived if the distributional tail of the random radius satisfies certain second-order regularly varying conditions. Numerical analysis with several examples is given to illustrate the decay rates.

Keywords: Bivariate skew elliptical distribution; Convergence rate; Second-order regular variation; Primary 62E20; 60G70; Secondary 60F15; 60F05 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11009-023-09986-1

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